模理论的Grothendieck环
Grothendieck Rings of Theories of Modules
摘要：
模型论的Grothendieck环的一阶结构，定义的Krajiclouk和Scanlon，捕捉一些组合性质的可定义子集的有限权力的结构。本文计算了右$R$ -模$M$的Grothendieck环，$K_0(M_\mathcal R)$，其中$\mathcal R$是任何单位环.作为推论，我们证明了Prest的一个猜想：当$M$非零时，$K_0(M)$是非平凡的.主要的证明使用了单纯复形的同调论中的各种技术。
英文摘要：
The model-theoretic Grothendieck ring of a first order structure, as defined by Krajicěk and Scanlon, captures some combinatorial properties of the definable subsets of finite powers of the structure. In this paper we compute the Grothendieck ring, $K_0(M_\mathcal R)$, of a right $R$-module $M$, where $\mathcal R$ is any unital ring. As a corollary we prove a conjecture of Prest that $K_0(M)$ is non-trivial, whenever $M$ is non-zero. The main proof uses various techniques from the homology theory of simplicial complexes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
